høyeredimensjonal

Høyeredimensjonal is an adjective used in Norwegian to describe something that involves or pertains to higher dimensions, typically more spatial dimensions than the familiar three. In mathematics and physics the term is applied to spaces and models with dimension greater than three, or to theories that extend spacetime beyond the usual four dimensions. The word combines elements meaning higher and dimensional, reflecting its role in describing objects and concepts beyond everyday three-dimensional space.

In mathematics, høyeredimensjonale spaces include Euclidean spaces R^n with n greater than three, manifolds of dimension n, and various abstractions such as high-dimensional vector spaces. These objects are central to geometry, topology, linear algebra, and analysis, and they provide a framework for studying properties that do not depend on low-dimensional intuition. In physics, higher-dimensional models extend the conventional four-dimensional spacetime and can appear in theories like string theory or extra-dimensional cosmologies, where additional spatial or temporal dimensions are hypothesized.

In data science and computer science, the term is often used to describe datasets with many features, i.e., high-dimensional data. Such data can lead to challenges known as the “curse of dimensionality,” where volume, sparsity, and computational complexity grow rapidly with dimension. Techniques for managing høyeredimensjonale data include dimensionality reduction (for example, principal component analysis or manifold learning) and feature selection. Related terms include dimensionality, hyperspace, and Hilbert space.